With the second edition of my Stanford MOOC Introduction to Mathematical
Thinking starting this weekend on Coursera, I have once again been
wrestling with the question of the degree to which good, effective mathematics
learning can be achieved at scale, over the Internet.

Once I had made the decision to try to take (elements of) my
35-year-old mathematics transition course into the then emerging MOOC
format—less than a year ago!—I was
immediately brought face-to-face with the necessity of making use of two
educational devices I had loathed (and never used) throughout my entire career
in higher education:

machine-graded pop quizzes

machine-graded multiple-choice questions

For MAA readers, I don’t think I need to explain my dislike
for either of these über-simplistic devices, which can surely be justified in a
regular classroom only in terms of making life easier for the instructor.

Simply putting a class online does not require the use of
either device, of course. Technologies such as video conferencing and screen
sharing can make learning at a distance almost as good as traditional classroom
learning, and in some circumstances can make it better in some respects. But making a class available to tens of thousands of students online
changes everything. With such large numbers, the “class” dynamics change
dramatically. But it’s not all for the worse.

The first thing to realize is that a MOOC is in many ways
like radio or TV. Though both of those familiar features of modern life are
referred to as “mass media,” they are in fact highly individual. The newsreader
on radio or TV is not addressing a large audience; she or he is talking to
millions of single individuals. The
secret to being good on the radio or TV is to forget the millions and think of
just one (generic) person. After all, the listener or viewer is not in a room
with millions of other people; in fact, if the broadcast is successful, that
listener or viewer is cognitively in a room with
just the presenter. The really successful radio and TV newsreaders and
presenters are the ones who can do that really well. They create that sense
that they are talking just to You.

In my own case, I already knew that from many years of
occasional media work, but I think all MOOC instructors come to that
realization very quickly. When your voice, with or without your face, is in
someone’s living room, there is a direct human connection that in important
ways is far more intimate than is possible in a lecture hall filled with
anything more than a handful of students.

Once you realize this feature of the MOOC medium, the
underlying pedagogic model is obvious. It’s one-on-one teaching/learning—something that in the traditional academy is (of necessity) reserved only for
doctoral students.

At which point, the appropriate use of both pop quizzes and
multiple-choice questions starts to look feasible. (They ought to; doctoral
advisers use both extensively, and to great positive effect, though they do not
refer to them as such, and there is no machine-grading!)

Of course, in a MOOC it remains the case that the student
cannot communicate directly with the professor, nor can the professor see and
comment on an individual student’s work. That means two further techniques have
to be used as well:

peer tutoring

peer evaluation

In the first version of my MOOC, last September, I built the
course around the doctoral-student education model, deliberately setting out to
create the experience of a student sitting alongside me at my desk. (There is a
low resolution example here.)

But as a result of a career-long dislike of the first two
and a deep suspicion of the fourth, I used all but the third of those auxiliary
devices reluctantly and as little as possible. (The one I did embrace, peer
tutoring, did not work well the way I set it up. See below for details of Attempt
Two.)

Because of my caution, I think I avoided a fate reminiscent
of NASA’s first attempts to launch a rocket into space. But that was a first,
exploratory experience, and I wanted to live to try again. This time around,
based on what I learned, I am going to use all four much more aggressively, but
in ways I think might work.

I’ll be describing how I’ll be using them in a series of
posts to my blog MOOCtalk.org. For a brief—and decidedly limited—foretaste, check out this video excerpt of a
conversation my MOOC TA Paul Franz and I had recently with radio and TV
personality Angie Coiro, host of the syndicated radio and television
interview show In Deep.

The goal of Version 2 of the course is not to
reach the Moon. Chances are high that we’ll crash and burn. The goal is to at least
get off the ground before we do, and, if we are lucky, maybe even reach the
upper atmosphere. For sure, there will still be a long way to go.

If you want to live dangerously and be part of
this huge experiment, and if you have a Ph.D. (or pending Ph.D.) in mathematics and
several years of college teaching behind you, I am still looking for well
qualified volunteers to act as “Community TAs” for the course, to answer
students' questions on the course discussion forums. So far I have 14
volunteers, comprising 5 college professors, 3 Ph.D. students, 3
individuals currently working in the software industry, a K-12 education
consultant, a research laboratory scientist, and a stock analyst. If you want
to volunteer, and have the requisite experience, please drop me an email at devlin@stanford.edu. (There is no payment
for doing this—that includes me!) But being part of a large and truly global
community, who come together for several weeks for the sole purpose of
learning how to think mathematically (the course carries no college credit), is
truly a wonderful experience.

Subscribe To

Follow by Email

About Me

The Mathematical Association of America is the world's largest community of mathematicians, students, and enthusiasts. We accelerate the understanding of our world through mathematics, because mathematics drives society and shapes our lives. Visit us at maa.org.